# List five rational numbers between $\dfrac{{ - 4}}{5}and\dfrac{{ - 2}}{3}.$

Last updated date: 22nd Mar 2023

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Answer

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Hint: Try to make the denominators same for both the given numbers.

In this question we have to find the rational numbers between $\dfrac{{ - 4}}{5}and\dfrac{{ - 2}}{3}.$

So we have given two numbers over to us i.e $\dfrac{{ - 4}}{5}and\dfrac{{ - 2}}{3}.$

Now in order to find the rational numbers between $\dfrac{{ - 4}}{5}and\dfrac{{ - 2}}{3}.$ we have to make the denominators same of both the numbers and hence for that we’ll multiply

${\text{,}}\dfrac{3}{3}{\text{ with }}\dfrac{{ - 4}}{5}{\text{ and }}\dfrac{5}{5}with{\text{ }}\dfrac{{ - 2}}{3}.$

And hence we have

$ \Rightarrow \left( {\dfrac{{ - 4}}{5} \times \dfrac{3}{3}} \right){\text{ and }}\left( {\dfrac{{ - 2}}{3} \times \dfrac{5}{5}} \right)$

$ = \dfrac{{ - 12}}{{15}}and\dfrac{{ - 10}}{{15}}$

So in this case we’ll have only 1 rational number between $\dfrac{{ - 12}}{{15}}and\dfrac{{ - 10}}{{15}}$ but we need a list of 5 rational numbers and hence we’ll multiply both the numbers

with $\dfrac{3}{3}$, so now we have

$ \Rightarrow \left( {\dfrac{{ - 12}}{{15}} \times \dfrac{3}{3}} \right)and\left( {\dfrac{{ - 10}}{{15}} \times \dfrac{3}{3}} \right)$

and hence on doing the multiplication, we have

$ \Rightarrow \dfrac{{ - 36}}{{45}}and\dfrac{{ - 30}}{{45}}$

So 5 Rational numbers between $\dfrac{{ - 36}}{{45}}and\dfrac{{ - 30}}{{45}}$ are $\dfrac{{ - 31}}{{45}},\dfrac{{ - 32}}{{45}},\dfrac{{ - 33}}{{45}},\dfrac{{ - 34}}{{45}},\dfrac{{ - 35}}{{45}}$.

Note: In this type of question we have to find the rational numbers between two given numbers and hence for that we’ll try to make the denominators same of those two given numbers and hence we can find the list of rational numbers between them.

In this question we have to find the rational numbers between $\dfrac{{ - 4}}{5}and\dfrac{{ - 2}}{3}.$

So we have given two numbers over to us i.e $\dfrac{{ - 4}}{5}and\dfrac{{ - 2}}{3}.$

Now in order to find the rational numbers between $\dfrac{{ - 4}}{5}and\dfrac{{ - 2}}{3}.$ we have to make the denominators same of both the numbers and hence for that we’ll multiply

${\text{,}}\dfrac{3}{3}{\text{ with }}\dfrac{{ - 4}}{5}{\text{ and }}\dfrac{5}{5}with{\text{ }}\dfrac{{ - 2}}{3}.$

And hence we have

$ \Rightarrow \left( {\dfrac{{ - 4}}{5} \times \dfrac{3}{3}} \right){\text{ and }}\left( {\dfrac{{ - 2}}{3} \times \dfrac{5}{5}} \right)$

$ = \dfrac{{ - 12}}{{15}}and\dfrac{{ - 10}}{{15}}$

So in this case we’ll have only 1 rational number between $\dfrac{{ - 12}}{{15}}and\dfrac{{ - 10}}{{15}}$ but we need a list of 5 rational numbers and hence we’ll multiply both the numbers

with $\dfrac{3}{3}$, so now we have

$ \Rightarrow \left( {\dfrac{{ - 12}}{{15}} \times \dfrac{3}{3}} \right)and\left( {\dfrac{{ - 10}}{{15}} \times \dfrac{3}{3}} \right)$

and hence on doing the multiplication, we have

$ \Rightarrow \dfrac{{ - 36}}{{45}}and\dfrac{{ - 30}}{{45}}$

So 5 Rational numbers between $\dfrac{{ - 36}}{{45}}and\dfrac{{ - 30}}{{45}}$ are $\dfrac{{ - 31}}{{45}},\dfrac{{ - 32}}{{45}},\dfrac{{ - 33}}{{45}},\dfrac{{ - 34}}{{45}},\dfrac{{ - 35}}{{45}}$.

Note: In this type of question we have to find the rational numbers between two given numbers and hence for that we’ll try to make the denominators same of those two given numbers and hence we can find the list of rational numbers between them.

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